Problem: Solve for $x$ and $y$ using elimination. ${3x-y = 14}$ ${-4x+y = -19}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {3x-y = 14}\thinspace$ to find $y$ ${3}{(5)}{ - y = 14}$ $15-y = 14$ $15{-15} - y = 14{-15}$ $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ You can also plug ${x = 5}$ into $\thinspace {-4x+y = -19}\thinspace$ and get the same answer for $y$ : ${-4}{(5)}{ + y = -19}$ ${y = 1}$